ALGEBRA QUESTIONS AND ANSWERS

Published: 2021-07-07 00:11:04
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Question: 67 INVESTMENTSAnswer:Assume X = amount in stocksInheritance amount= 24,000Advisor’s recommended ratio = 3/5Based on the provided data; formulated the following equation24000=3/5 multiply by x+ x24000= 8/5 (x) and by further arranging the like terms of the equation we get24000* 5/8+ x or x= 24000* 5/8And therefore x=15000Checking the answers:Assessing the validity of the answer requires putting the estmated amount of x in the initial equation.24,000=3/5 (15,000) + (15,000)By calculating this, it becomes evident that LHS is equal to RHS24,000=24,000And therefore the answer is true. And 15,000 subtracted from 24,000 makes it 9000 that should be invested in bonds. According to the calculation it is recommended to invest 15,000 in stocks and 9000 in bonds.Question 71: BANKINGAnswer:For this loan problem let the fraction (f) of 500,000 dollars be loaned at 6 percent meanwhile for the rest of it be 1-f at 11 percent per annum. Therefore the total interest is:6/100*500,000(f) + (1+f) * 500,000 *11/100 = 30000(f) and30,000(f) + 55,000(1-f) = 55,000 so55000-25,000(f) = 43750For this reason 25,000(f) = 11,250 and/or f=45/100=0.45Therefore the amount loaned at 6% is the:500,000(f) = 225,000Question 73:INVESTMENTSAnswer:Let’s suppose x= amount to be invested at 5%And the investment amount at 9% is x-25,000In this context the sum of interest earned is:0.05*x + 0.09 * (25,000-x) =1,8750.05*x + 2,250-0.09*x =1,875 so-0.04*x =-375X= 9,375Therefore, 9,375 dollars are the amount to be invested at 5%Checking answer:0.05*9,375+0.09*15625=468.75 and468.75+ 1406, 25 = 1,875Question 76:CANDYAssumex= numbers of pounds almonds = 40 IbsY= numbers of pounds peanuts =10 IbsAnd therefore we get the equation:X=50-yBy arranging the equation:X+y = 506.50(x) + 4.00(y) = 6.00 (50)And by suing substitution:X=y = 506.50x+ 4(y) = 3006.50 (50-y) + 4(y) =300325-6.50y+4(y)=300325-2.50y=300-2.50(y) =-25And thereforeY= 10By putting the value of y in the equation we get:X+10=50X=40Question 77COINSX= number of quartersY= number of dimesX+y = 47And y=47-xTherefore .25+.10y=9.50.25x+.10(y) =9.50.25x+4.7-.10x=9.50.15(x) + 4.7= 9.50-4.7-4.70.15(x)/.15= 4.8/.15X=32Y = 47-32In this way the value of y becomesY=15That’s makes it evident that bobby has 15 dimes and 32 quarters.Question 89ANTIFREEZELet’s suppose V= volume of antifreeze (40%)And 15-V=volume of pure antifreeze (100%) requiredIt is evident that last antifreeze composition was 15 litre of antifreeze (50%).For this situation save V 40% antifreeze liters and combine it with 15-V 100% antifreeze liters. For this purpose:40% (V) =100% (15-V) = 50% (15)To convert the percentage0.4 V + 1.0 (V-15) = 0.5 (15) so.4 V + 1.0 (15)-1.0 V =7.5By combining the like terms:.4(v) – 1.0 (v) +15=7.5-0.6(v)+15 =7.5-0.6(v) =7.5-15-0.6(v) -7.5V=12.5 litre of anitfreeze (40%)15-v= 2.5 liter of antifreeze pure(100%)

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